rendering problems in blender
This is a common issue, it's called "Fireflies" by the community and there are a lot of ways of dealing with them. 

Here's one good article, but before you dive into it let's discuss where they come from in the first place.

Cycles is a PathTracer. For each pixel it sends out a bunch of light rays from the camera, bounces them around and then sees where they end up to determine the color of the pixel. This works because physics doesn't really care if times is going forwards of backwards in this case. 

You can determine how often a light ray bounces around by adjusting the "Samples" option in the render tab. Try 100, 200, 300 and so on - more samples means more calculations means more render time, but also less fireflies and noise in the image. 

An alternative to that is the "Denoiser", which you can find in the "Render Layers" tab on the right. It's a tradoff between quality and performance, give it a shot if your render times are too long.